Bond Order

The bond order (B.O.) in diatomic molecules is half of the difference between the total numbers of the bonding electron (N_b) and antibonding electrons (N_a) therefore

B.O. = \dfrac{N_b- N_a}{2}
  • If bond order is zero, the molecule does not exist.
  • \text{ Bond order }\propto \text{Bond angle} \propto \text{Bond energy} \\ \propto \dfrac{1}{\text{Bond length}}

Molecular orbital configuration of some homonuclear diatomic molecules and ions with their bond order etc, are given here.

1. H_2 : \sigma (1s)^2 \hspace{20mm} B.O. = \dfrac{2- 0}{2} = 1

Bond energy of H_2 \text{is} 436 kJ \text{mol}^{-1} and bond length is 0.751 \AA

2. H^+_2 : \sigma(1s))^1 \hspace{20mm} B.O. = \dfrac{1- 0}{2} = \dfrac{1}{2}

Bond energy of ^+_2 \text{is} 269 kJ \text{mol}^{-1} and bond length is 1.04 \AA

3. He_2 : \sigma (1s)^2 \hspace{20mm} B.O. = \dfrac{2- 2}{2} = 0

Since bond order of helium molecule (He_2) is zero hence helium does not exist as He_2

4. Li_2 : \sigma (1s)^2 \sigma^*(1s)^2 \sigma (2s)^2; \; \; B.O. = \dfrac{4- 2}{2} = 1

The bond energy of Li_2 molecule is low (105kJ \text{mol}^{-1}) and its bond length is larger 2.67\AA.


Bond order


5. Be_2 : \sigma (1s)^2 \sigma^* (1s)^2 \sigma (2s)^2 \sigma^* (2s)^2; \\ B.O. = \dfrac{4- 4}{2} = 0

Since in this case, again bond order is zero hence beryllium does not exist as Be_2. It exists as Be.

6. B_2 : \sigma (1s)^2 \sigma^* (1s)^2 \sigma (2s)^2 \pi )2p_x)^1 \pi(2p_y)^1; \\ B.O. = \dfrac{6- 4}{2} = 1

The bond energy of B_2 molecule is 289kJ \text{mol}^{-1} and its bond length is 1.59 \AA. This molecule is paramagnetic due to the presence of unpaired electrons.

7. C_2 : \sigma (1s)^2 \sigma^* (1s)^2 \sigma (2s)^2 \sigma^* (2s)^2 \pi (2p_x)^2 \pi (2p_y)^2 \\ B.O. = \dfrac{8- 4}{2} = 2

Its bond energy and bond length are found to be 606.7kJ \text{mol}^{-1} and 1.31 \AA, respectively.

8. N_2 \sigma (1s)^2 \sigma^* (1s)^2 \sigma (2s)^2 \sigma ^* (2s)^2 \pi (2p_x)^2 \pi (2p_y)^2 \sigma(2p_z)^2 \\ B.O. = \dfrac{10- 4}{2} = 3, i.e., N \equiv N

Its bond energy and bond length are 945.6 kJ \text{mol}^{-1} and 1.10 \AA respectively.

This order of enrgy level is followed by H, He, Li, Be, B, C and N. this is due to the mixing of 2s and 2p_zAOs. This mixing is not possible in the case of oxygen, fluorine etc. because in these case the difference between energies of 2s and 2p_z AOs is larger. Therefore the order of energy level of oxygen, fluorine etc. molecular orbitals is given below and shown in figure

\sigma (1s) < \sigma^* (1s) < \sigma (2s) < \sigma^* (2s) < \sigma (2p_z) < \pi (2p_x) = \pi(2p_x) < \pi^* (2p_x) = \pi^* (2p_y) < \sigma^*(2p_z)


Bond order


9. O_2 \sigma (1s)^2 \sigma ^* (1s)^2 \sigma (2s)^2 \sigma ^* (2s)^2 \sigma (2p_z)^2 \pi (2p_x)^2 \pi (2p_y)^2 \pi ^* (2p_x)^1 \pi ^* (2p_y)^1 \\ B.O. = \dfrac{10 - 6}{2} = 3, \\ i.e., O \equiv O

Its bond energy is 494.6 kJ \text{mol}^{-1} and bond length is 1.21 \AA . Since there are more antibonding electrons than N_2 hence it is less stable than N_2. Due to the presence of unpaired electrons it is paramagnetic in nature.

10. F_2 : \sigma (1s)^2 \sigma^* (1s)^2 \sigma (2s)^2 \sigma ^* (2s)^2 \sigma (2p_z)^2 \pi (2p_x)^2 \pi (2p_y)^2 \pi^* (2p_x)^2 \pi^* (2p_y)^2 \\ B.O. = \dfrac{10- 8}{2} = 1, i.e., e - F - F\equiv O

Its bond energy and bond length are 155 kJ \text{mol}^{-1} \text{and} 1.42 \AA respectively. This is also more reactive than N_2 \text{and} O_2 due ot more antibonding electrons.

11. Ne_2 : \sigma (1s)^2 \sigma^* (1s)^2 \sigma (2s)^2 \sigma ^* (2s)^2 \sigma (2p_z)^2 \pi (2p_x)^2 \pi (2p_y)^2 \pi^* (2p_x)^2 \pi^* (2p_y)^2 \pi^* (2p_z)^2 \\ B.O. = \dfrac{10- 10}{2} = 0

Since in this case bond order is zero hence neon does not exist as Ne_2. It exists as Ne.

Related posts:

  1. Bond lenght, angle and energy Bond length, Bond angle and Bond energy Since atoms in...
  2. Molecular Orbital Theory Molecular Orbital Theory (MOT) [Based on Linear Combination of Atomic...
  3. Sigma and Pi Bonds Sigma and Pi Bonds According to orbital theory, covalent bond...
  4. Odd Electron Bond Odd Electron Bond It may be defined as, "The bonds...
  5. Valence Bond Theory Actually speaking treatment of the covalent bond is far more...